
Krylov solvability under perturbations of abstract inverse linear problems
When a solution to an abstract inverse linear problem on Hilbert space i...
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Regularising linear inverse problems under unknown nonGaussian white noise
We deal with the solution of a generic linear inverse problem in the Hil...
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Krylov solvability of unbounded inverse linear problems
The abstract issue of 'Krylov solvability' is extensively discussed for ...
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A conjugategradienttype rational Krylov subspace method for illposed problems
Conjugated gradients on the normal equation (CGNE) is a popular method t...
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Joint Inverse Covariances Estimation with Mutual Linear Structure
We consider the problem of joint estimation of structured inverse covari...
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A stochastic algorithm for fault inverse problems in elastic half space with proof of convergence
A general stochastic algorithm for solving mixed linear and nonlinear pr...
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Stein variational gradient descent on infinitedimensional space and applications to statistical inverse problems
For solving Bayesian inverse problems governed by largescale forward pr...
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Inverse linear problems on Hilbert space and their Krylov solvability
This monograph is centred at the intersection of three mathematical topics, that are theoretical in nature, yet with motivations and relevance deep rooted in applications: the linear inverse problems on abstract, in general infinitedimensional Hilbert space; the notion of Krylov subspace associated to an inverse problem, i.e., the cyclic subspace built upon the datum of the inverse problem by repeated application of the linear operator; the possibility to solve the inverse problem by means of Krylov subspace methods, namely projection methods where the finitedimensional truncation is made with respect to the Krylov subspace and the approximants converge to an exact solution to the inverse problem.
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